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V. P. Neznamov

Publications and source records attributed to V. P. Neznamov.

At least 19 recordsLinked to original sources
arXiv2026

Mathematical Paradoxes of Dirac Equation Representations

This paper examines the Foldy-Wouthuysen and Feynman-Gell-Mann representations of the Dirac equation. The analysis is conducted for electrons and positrons interacting with electromagnetic fields. Versions of quantum electrodynamics are considered both within the scope of perturbation theory and in the nonperturbative case with strong electromagnetic fields. Mathematical artifacts that contradicting the physical premises of the theory are identified in the studied representations of the Dirac equation. These mathematical paradoxes are resolved if the theory only employs amplitude states (real and virtual) with positive energies.

hep-th↗
arXiv2025

The possibility to experimentally determine the structure of a fermionic vacuum in quantum electrodynamics

In the standard quantum electrodynamics (QED), the fermionic vacuum is a continuum of randomly created and annihilated virtual electron-positron pairs. In this case, in the strong electromagnetic fields, vacuum creation of real electron-positron pairs is possible. In particular, in the standard QED in a strong uniform electrical field, the Schwinger effect is implemented. Currently, there exist the QED versions with empty fermionic vacuum without fluctuations of creation and annihilation of virtual electron-positron pairs. These versions are the (QED)FW in the Foldy-Wouthuysen representation, the $(QED)_{KG}$ with spinor equations of the Klein-Gordon type, the $(QED)_{DN}$ with opposite signs in front of particle and antiparticle masses in Dirac equations and with the use of only states with positive energies in S-matrix elements. The latter relates to both real and virtual energy states. In this paper, we propose to carry out a set of experiments at colliders with collisions of heavy ions to determine the nature of the fermionic vacuum. The measurements of the emission of electron-positron pairs depending on the total charge of colliding ions $Z_Σ = 146 ÷184$ show the structure of a fermionic vacuum in quantum electrodynamics.

hep-ph↗
arXiv2025

Closed Foldy-Wouthuysen transformations for fermions moving in gauge-invariant time-dependent electromagnetic fields

Previously, we obtained closed expressions for energy operators in the Foldy-Wouthuysen representation in the presence of static electric fields. In this case, we also established a connection between the Foldy-Wouthuysen representation and the Feynman-Gell-Mann representation. In this work, we generalize these results for the case of fermions moving in time-dependent gauge-invariant electromagnetic fields.

hep-th↗
arXiv2024

The Quantum Model of Spinning Black Holes

We propose a quantum model of spinning black holes with the integrable ring singularities. For the charged Kerr-Newman quantum metric, the complete regularization takes place at fixing of the maximal (cut-off) energy of gravitons, $k_{UV}^{reg} = \hbar c/R_{S}^{reg}$.The domains of existence of one, two and several event horizons $r_{q}$ are shown depending on the parameters of modified Kerr and Kerr-Newman metrics.

gr-qc↗
arXiv2023

Quantum probing of singularities at event horizons of black holes

It is proved that coordinate transformations of the Schwarzschild metric to new static and stationary metrics do not eliminate the mode of a particle ''fall'' to the event horizon of a black hole. This mode is unacceptable for the quantum mechanics of stationary states.

gr-qc↗
arXiv2023

Something new about radial wave functions of fermions in the repulsive Coulomb field

An impermeable barrier at $r=r_{cl}$ in the effective potential of the relativistic Schrödinger-type equation leads to exclusion of the range $0 \leq r < r_{cl}$ from the wave function domain. Based on duality of the Schrödinger-type equation and the Dirac equation, a similar exclusion should be made in the wave functions domain of the Dirac equation. As a result, we obtain new solutions to the Dirac equation in the Coulomb repulsive field. Calculations show that depending on working parameters, at distances of several fractions or units of the Compton wavelength of the fermion from $r=r_{cl}$ new solutions almost coincide with the standard Coulomb functions of the continuous spectrum. Practically, matrix elements with new solutions will coincide to a good accuracy with standard matrix elements with the Coulomb functions of the continuous spectrum. Our consideration is methodological and helpful for discussing further development of quantum theory.

quant-ph↗
arXiv2021

The lack of vacuum polarization in quantum electrodynamics with spinors in fermion equations

In this paper, the versions of quantum electrodynamics (QED) with spinors in fermion equations are briefly examined. In the new variants of the theory, the concept of vacuum polarization is unnecessary. The new content of fermion vacuum (without the Dirac sea) in the examined versions of QED leads to new physical consequences, part of which can be tested experimentally in the future.

physics.gen-ph↗
arXiv2021

Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED.Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particle and anti-particles have the opposite signs.

physics.gen-ph↗
arXiv2020

Quantum mechanics of stationary states of particles in a space-time of classical black holes

We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman gravitational and electromagnetic fields with a zero and nonzero cosmological constant. We also consider interactions of scalar particles, photons, and fermions with nonextremal rotating charged black holes in a minimal five-dimensional gauge supergravity. We analyze the behavior of effective potentials in second-order relativistic Schrödinger-type equations. In all cases, we establish the existence of the regime of particle "falling" on event horizons. An alternative can be collapsars with fermions in stationary bound states without a regime of particles "falling".

physics.gen-ph↗
arXiv2020

Quantum mechanics of stationary states of particles in external singular spherically and axially symmetric gravitational and electromagnetic fields

The report considers the interaction of scalar particles, photons and fermions with the gravitational and electromagnetic Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman fields. The behavior of effective potentials in the relativistic Schrödinger-type second-order equations is analyzed. It was found that the quantum theory is incompatible with the hypothesis of the existence of classical black holes with event horizons of zero thickness that were predicted based on solutions of the general relativity (GR) with zero and non-zero cosmological constant $Λ$. The alternative may be presented by compound systems, i.e., collapsars with fermions in stationary bound states.

physics.gen-ph↗
arXiv2019

Second-order stationary solutions for fermions in an external Coulomb field

We have studied self-conjugate second-order equations with spinor wavefunctions for fermions moving in an external Coulomb field. For stationary states, the equations are characterized by separated states with positive and negative energies, which render probabilistic interpretation possible. For the Coulomb field of attraction, the energy spectrum of the second-order equation coincides with the spectrum of the Dirac equation, while the probability densities of states are slightly different. For a Coulomb field of repulsion, there exists an impermeable potential barrier with radius depending on the classical electron radius and on the electron energy. The existence of the impermeable barrier does not contradict the results of experiment for determining the inner electron structure and does not affect (in the lowest order of perturbation theory) the Coulomb electron scattering cross section. The existence of the impermeable barrier can lead to positron confinement in supercritical nuclei with $Z \geq 170$ in case of realization of spontaneous emission of vacuum electron-positron pairs.

physics.gen-ph↗
arXiv2019

Quantum mechanical equivalence of the metrics of a centrally symmetric gravitational field

We analyze the quantum mechanical equivalence of the metrics of a centrally symmetric uncharged gravitational field. We consider the static Schwarzschild metric in spherical and isotropic coordinates, the stationary Eddington-Finkelstein and Painlevé-Gullstrand metrics, and nonstationary Lemaître-Finkelstein and Kruskal-Szekeres metrics. When the real radial functions of the Dirac equation and of the second-order equation in the Schwarzschild field are used, the domain of wave functions is restricted to the range $r>r_{0}$, where $r_{0}$ is the radius of the event horizon. A corresponding constraint also exists in other coordinates for all considered metrics. For the considered metrics, the second-order equations admit the existence of degenerate stationary bound states of fermions with zero energy. As a result, we prove that physically meaningful results for a quantum mechanical description of a particle interaction with a gravitational filed are independent of the choice of a solution for the centrally symmetric static gravitational field used.

physics.gen-ph↗
arXiv2019

Stationary solutions of the second-order equation for fermions in Kerr-Newman space-time

When using the quantum mechanical second-order equation with the effective potential of the Kerr-Newman (KN) field for fermions, results were obtained that qualitatively differ from results obtained when using the Dirac equation. In presence of two event horizons, existence of degenerate stationary bound states was proved for charged and uncharged fermions with square integrable wave functions vanishing on event horizons. The fermions in such states are localized near the event horizons with the maxima of probability densities away from the event horizons by fractions of the Compton wave length of fermions versus the values of coupling constants, the values of angular and orbital momenta $j,l$ and the value of the azimuthal quantum number $m_φ$. In the case of extreme KN fields, absence of stationary bound states of fermions was shown for any values of coupling constants. Existence of discrete energy spectra was shown for charged and uncharged fermions in the field of naked KN singularity at definite values of physical parameters. The KN naked singularity poses no threat to cosmic censorship because of the regular behavior of the effective potentials of the KN field in quantum mechanics with the second-order equation.

gr-qc↗
arXiv2018

Stationary solutions of second-order equations for fermions in Reissner-Nordström space-time

Existence of degenerate stationary bound states with square integrable radial wave functions was proved when second-order equations are used with the effective potential of the Reissner-Nordström (RN) field with two event horizons for charged and uncharged fermions. The fermions in such states are localized near event horizons within the ranges from zero to several fractions of Compton wave length of fermions versus the values of gravitational and electromagnetic coupling constants and the values of angular and orbital momenta $j,l$. In case of extreme RN fields, absence of stationary bound states of fermions with the energies of $E<mc^{2}$ is shown for solutions of the second-order equation for any value of gravitational and electromagnetic coupling constants. Existence of the discrete energy spectrum is shown for the naked RN singularity due to solution of the second-order equation at definite values of physical parameters. The discrete spectrum exists for both charged and uncharged fermions. The naked RN singularity in quantum mechanics with the second-order equation for half-spin particles poses no threat to cosmic censorship since it is covered with an infinitely large potential barrier. Electrically neutral systems of atomic type (RN collapsars with the definite number of fermions in degenerate bound states) are proposed to consider as particles of dark matter.

gr-qc↗
arXiv2018

Stationary solutions of second-order equations for point fermions in the Schwarzschild gravitational field

When using a second-order Schrödinger-type equation with the effective potential of the Schwarzschild field, existence of a stationary state of half-spin particles with energy $E=0$ is proved. For each of the values of quantum numbers $j,l$, the physically meaningful energy $E=0$ (the binding energy is $E_{b}=mc^{2}$) is implemented at the value of the gravitational coupling constant $α\geqα_{min}$. The particles with $E=0$ are, with the overwhelming probability, at some distance from the event horizon within the range from zero to several fractions of Compton wavelength of a fermion depending on value of the gravitational coupling constants and values $j,l$. In this paper, similar solutions of the second-order equation are announced for bound states of fermions in the Reissner-Nordström, Kerr, Kerr-Newman fields. Atomic-type systems: collapsars with fermions in bound states are proposed as particles of dark matter.

gr-qc↗
arXiv2018

Atomic systems with bound states of fermions in the Schwarzschild, Reissner-Nordström fields as candidates for the role of dark matters particles

After transition from the Dirac equation to the Schrödinger-type relativistic equation with effective potentials of the Schwarzschild and Reissner-Nordström (RN) fields, the existence of the stationary state of fermions with real square-integrable radial wave functions is proved. The fermions are localized near the event horizon within the range from zero to several fractions or a few units of the Compton wavelength of a fermion as a function of the gravitational and electromagnetic coupling constants and the angular and orbital momenta j,l. Electrically neutral atomic-type systems (Schwarzschild and RN collapsars with fermions in bound states) are proposed as particles of dark matter.

gr-qc↗